Problem: A circle with area $16\pi$ has a sector with a $207^\circ$ central angle. What is the area of the sector? ${16\pi}$ $\color{#9D38BD}{207^\circ}$ ${\dfrac{46}{5}\pi}$
Explanation: The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{207^\circ}{360^\circ} = \dfrac{A_s}{16\pi}$ $\dfrac{23}{40} = \dfrac{A_s}{16\pi}$ $\dfrac{23}{40} \times 16\pi = A_s$ $\dfrac{46}{5}\pi = A_s$